A business operating plant has a challenge with corrosion damage. They are considering

replacing the affected equipment at a cost of $$5M.($The new equipment is a better design and

will not corrode$).$ The damage rate has been $$1M$ per year but it could double or quadruple

each year. As their consultant, you are asked to model the multi$-$stage decisions for the next $2$

years.

You study the corrosion rates seen throughout the industry and conclude the most likely

corrosion rate probabilities in any one year are: steady is $60\%,$ double is $30\%$ and quadruple is

$10\%.$ You find that once the corrosion rate goes up in any year, that's the new base level

meaning that subsequent steady, double, or quadruple rates are from that value.

a$.$ Create an event tree model to analyze this multi$-$stage decision.

Please draw out the tree